The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for assessing grade-level content.

 Assessments are located in the Assessment Guide book. Assessments consist of a Prerequisite Skills Inventory, Middle-of-Year Test, End-of-Year Test, 18 Module Tests, and 6 Unit Performance Tasks. Each Module Assessment consists of a printable and interactive Form A and Form B.

The Interactive Middle of Year Test assesses the standards taught in approximately the first half of the year of Into Math Florida, and the Interactive End of Year Test assesses the full year of standards. For example, Middle of Year Test, Item 3, “Which of these shows how to use counting back to find 11 – 2?" (1.OA.1)

Module Tests are available digitally and in the Assessment Guide. Examples include:

• Module 3 Test, Forms A and B, Items 2, 3, and 5, students use the properties of operations as strategies to add and subtract. In Form A, Item 5, “What number will make the equation true? 4 + = 7 + 4.” (1.OA.3) 
• Module 6 Test, Forms A and B, Items 1-8, students solve addition and subtraction word Items within 20 involving situations of adding to, taking apart, putting together, with unknowns in all positions. In Form A, Item 3, “There are 16 children on the rug. There are 7 children standing. The rest are sitting. How many children are sitting on the rug? 16 =___ + 7, ____  children.” (1.OA.1) 
• Module 9 Test, Forms A and B, Item 2, students identify bundles of ten with given models. In Form B, Item 2, “How many groups of ten can be made from these blocks?” The picture shows 20 blocks arranged in a 4 by 5 array. (1.NBT.2.a) 
• Module 9 Test, Forms A and B, Items 3, 8, and 9, students use models to determine how many tens or asked to match a given number of tens as ___ tens and 0 ones. In Form B, Item 8, “Richard has 8 bags. He puts 10 blocks in each bag. How many blocks are in all the bags?”  (1.NBT.2c)
• Module 9 Test, Forms A and B, Items 4-6, students look at numbers 11-19 and select the correct answer of 1 ten and ___ ones. In Form B, Item 5, “Travis has 10 toy trucks. He gets 5 more toy trucks. How many toy trucks does Travis have now?____ ten _____ ones, _____ toy trucks.” (1.NBT.2b)
• Module 10 Test, Form A, Item 2, students count by ones to find a missing number. “Count by ones. What number is missing? 79, 80,___ , 82, 83?” (1.NBT.1)
• Module 12 Test, Items 1, 3, and 5, students add two-digit addends with single-digit addends to add within 100. In Form A, Item 3, “Liam has 14 baseball cards and 9 soccer cards. Which equation shows how many sports cards Liam has?” (1.NBT.4)
• Module 12 Test, Forms A and B, Items 7 and 8, students show ten more or ten less of a number using equations, word Items, or matching. In Form A, Item 7, “Draw a line from each number to the number that is 10 less. You will not use all the numbers.” (1.NBT.5)
• Module 12 Test, Forms A and B, Items 9 and 10, students solve word problems. In Form A, Item 10, “Noah sees 40 fish. There are 30 green fish. The rest are orange. How many orange fish does Noah see?” (1.NBT.6)
• Module 15 Test, Forms A and B, Items 1 and 2, students identify two-dimensional shapes using defining attributes and describe defining attributes. In Form A, Item 2, “Which shape has 6 sides and 6 vertices?” Students choose from a square, hexagon, and rectangle. (1.G.1) 
• Module 15 Test, Forms A and B, Items 3 and 6-7, students create composite shapes or identify shapes used to create composite shapes. In Form A, Item 3, “Which shape can be made by combining these 3 shapes?” (1.G.2)
• Performance Assessments with multiple tasks for each unit are provided in the Assessment Guide. Module 3 Task 2, “Jamal has some marbles. He has 28 green marbles. If the number of blue marbles is 10 more than the number of green marbles, how many blue marbles does Jamal have? Write how you know.” (1.NBT.4) 

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of Modules devoted to major work of the grade (including assessments and supporting work connected to the major work) is 15 out of 18, which is approximately 83%.
• The approximate number of Lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 87 out of 99, which is approximately 88%.
• The approximate number of days devoted to major work (including assessments and supporting work connected to the major work) is 129 out of 160, which is approximately 80%.

 A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each module. As a result, approximately 88% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Throughout the instructional materials, major work of the grade is supported by non-major work.

Module 8, Data, engages students with 1.MD.4, (Represent and interpret data). Throughout the module connections are made to the major work of 1.OA.A, (Represent and solve problems involving addition and subtraction), and 1.OA.C, (Add and subtract within 20). Examples of how the materials connect supporting work to the major work of the grade include: 

• In Lesson 1, More Practice/ Homework, the supporting work of 1.MD.4 is connected to the major work of 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.) as students solve Problem 3, “How many more starfish are there than shells?  Write an equation to show how you know.”
• In Lesson 4, More Practice/Homework, the supporting work of 1.MD.4 is connected to the major work of 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10), as students solve Problem 1, Use the picture (6 golf balls and 9 tennis balls) to make a tally chart. Problem 2, “How many sports balls does Jo have? Problem 3, Are there more golf balls or tennis balls?”
• In Lesson 6, Build Understanding, the supporting work of 1.MD.4 is connected to the major work of 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10) as students solve Problem C, “Are there more dogs or cats? How many more?  Equation:_____________.”
• In Lesson 7, On Your Own, Problem 2, the supporting work of 1.MD.4 is connected to the major work of 1.OA.2 (Solve word problems that call for addition of three whole numbers whose sum is less than 20) and 1.OA.6 (Add and subtract within 20) as students “Make a bar graph to show the problem. Then use the problem to solve: Some leaves fall from a tree. 9 leaves are red. There are 5 more red leaves than orange leaves. There are 2 fewer yellow leaves than orange leaves. How many leaves fell from the tree?”

Instructional materials reviewed for HMH Into Math Grade 1 meet expectations that the amount of content designated for one grade-level is viable for one year. 

As designed, the instructional materials can be completed in 160 days. The suggested amount of time and expectations for teachers and students in the materials are viable for one school year as written and would not require significant modifications.

• There are 115 days of instruction.
• There are 3 days per year for the Growth Measure Assessments.
• There are 6 Units. There is 1 day per Unit for the Performance Task total of 6 days.
• There are 18 Modules, with 1 day for each Module Opener, Are You Ready?, and 1 day for each Module Review and Module Test, for a total of 36 days.

The suggested pacing from the publisher is 1 day per lesson for most lessons. However, some lessons are listed for 2 days. There are no lessons that require more than 2 instructional days to complete. 

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for being consistent with the progressions in the Standards, providing all students with extensive work of the grade, and explicitly identifying prior knowledge needed for grade level work.

In the Planning and Pacing Guide, there is a Correlations Chart where all grade-level standards are represented. Tasks are aligned to grade-level work and are connected to prior knowledge. A typical lesson has Are You Ready? to assess student readiness for the upcoming module, Warm-Up Options, and Spark Your Learning activities intended to assist with activating prior knowledge. Build Understanding/Step It Out, On Your Own, and More Practice/Homework, which includes a Spiral Review, are available in most lessons. Additionally, every lesson provides Small Group Options or Math Center Options that can be used to plan for differentiated instruction.

 The instructional materials clearly identify for each module Teaching for Success that shows the progressions of the standards from “Prior Learning”, to “Current Development,” and to “Future Connections” respectively. In the beginning of each lesson, Mathematical Progressions include the same progressions with “Future Connections” explicit to the lesson. Examples of “Future Connections” include:

• Module 3, Lesson 2, Mathematical Progressions, Future Connections, “Children will add and subtract within 1,000, using strategies based on properties of operations (Grade 2, Lessons 13.6-13.7); Children will fluently add and subtract within 20 (Grade 2, Lessons 1.1-1).” 
• Module 6, Lesson 6, Mathematical Progressions, Future Connections, “Children will use addition and subtraction within 100 to solve word problems. (Grade 2, 14-3-14.5, 15.1-15.2); Children will solve two-step addition and subtraction word problems (Grade 2, Lesson 15.3).”
• Module 16, Lesson 4, Mathematical Progressions, Future Connections, “ Children will identify, describe, and draw two, three, or four equal shares. (Grade 2, Lessons 22.2-22.3); Children will identify these equal shares as halves, thirds, and fourths (quarters) (Grade 2, Lessons 22.2-22.3); children will use different ways to show halves, thirds, and fourths (quarters) (Grade 2, Lesson 22.5).” 

A typical lesson includes multiple opportunities for students to engage with extensive work of the grade. Build Understanding and Step It Out and Connect Concepts and Skills are intended to engage students with new grade-level content. During On Your Own (independent practice), and More Practice/Homework, students work with grade-level problems. For example:

• Unit 2 addresses Addition and Subtraction Situations and Data. Students engage with extensive work of the grade to understand “add to and take from” problems, “put together and take apart” problems, and comparison problems.
• Module 5, Lesson 4, On Your Own, Problem 2, “Bert has some markers. He gives 8 to Alex. Now he has 5 markers. How many markers did he have to start?” Students draw a picture and write an equation to represent the problem and find the number of markers.
• Module 6, Lesson 7, More Practice/Homework, Problem 2, students solve “The Beach Shop has 15 pails. The pails are red or blue. How many of each color could there be?”
• Module 7, Lesson 6, On Your Own, Problem 7, students solve comparison problems. “Ellen has 9 peaches. Saul has 14 peachers. How many fewer peaches does Ellen have than Saul? Draw a picture to show how to solve the problem.”
• Unit 5, Geometry, addresses two- and three-dimensional shapes, and introduces fraction foundations. 
• Module 14, Lesson 3, On Your Own, Problem 4, students compose new three-dimensional shapes. Students are given a picture of a 4 unit cube to solve “How can you make this shape using combined shapes?” Students can use unit cubes, rectangles, and other combined shapes to make the cube.
• Module 15, Lesson 5, On Your Own, Problem 2, students compose two-dimensional shapes. “Use 2 rectangles to make a square. Make a second square, just like the first. Put the 2 squares together to make another shape. What is the new shape?”
• Module 16 addresses fraction foundations. In Lesson 1, students take apart two-dimensional shapes. In Lesson 2, students explore equal and unequal shares. Lessons 3 and 4 students partition shapes into halves and fourths respectfully. Lesson 2, On Your Own, Problem 7, “Is half of a shape smaller or larger than the whole shape. Explain.” 

In addition to including Mathematical Progressions identifying prior learning for each lesson, the beginning of each module explicitly identifies and engages prior learning during the "Are You Ready?" activities designed to diagnose mastery, inform grouping and differentiation. Warm-Up Options in all lessons, and Spark Your Learning activities in Build Understanding and Connect Concepts and Skills lessons are intended to assist with activating prior knowledge. Examples include:

• Module 3, Are You Ready?, includes ways to make 5  (K.CC.4b), using symbols to add (K.OA.1) and drawing equal groups (K.CC.6). Problem 1, Use connecting cubes. “Show different ways to make 5. Color what you did.”
• In Module 10, Lesson 5, Mathematical Progressions, Prior Learning is identified. “Children used tens and ones to represent numbers to 20 (Grade K, 17.1, 17.2, 17.3, 17.4, 18.1, 18.2, 18.3).”
• In Module 18, Lesson 4, Spark You Learning, students show times on a clock. “Activate prior knowledge but showing children images of clocks. Ask: Which is the hour hand? Which is the minute hand? How can you tell which is the hour hand? How does the minute hand differ from the hour hand?”

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The materials include learning objectives that are visibly shaped by CCSSM cluster headings, including:

• In Module 2, Lesson 3, the Learning Objective, “Use counting on as a strategy to solve basic subtraction facts,” is shaped by 1.OA.C, (Add and subtract within 20).
• In Module 13, Lesson 2, the Learning Objective, “Add two-digit numbers within 100 using place value,” is shaped by 1.NBT.C, (Use place value understanding and properties of operations to add and subtract).
• In Module 14, Lesson 2, the learning objective, “Combine three-dimensional shapes to make composite shapes,” is shaped by 1.G.A, (Reason with shapes and their attributes).

The materials include problems and activities connecting two or more clusters in a domain or two or more domains in a grade, in cases where these connections are natural and important, and examples of this include:

• In Module 4, Lesson 1 , On Your Own  connects 1.OA.A, and 1.OA.C as students solve problems involving addition and subtraction and add and subtract within 20. Step It Out, Problem 2, “There are 13 birds in a tree. 9 are red. The rest are blue, How many blue birds are in the tree? Use addition to solve 13 - 9 = __. A. Use the numbers from the subtraction problem to write an addition equation.”
• Module 12, Lesson 1, Build Understanding, connects 1.NBT.B with 1.NBT. as students develop their understanding of place value and use that understanding to add and subtract. Task 1, “The Beach Shop has 30 adult sunglasses and 40 child sunglasses. B. How many sunglasses does the shop have? A. How can you show the problem? How can you write an equation to solve the problem? C. The shop has __ sunglasses.”
• In Module 13, Lesson 2, connects 1.NBT.C  and 1. NBT.B as students solve addition problems using place value understanding. Check Understanding, Problem 1, “Draw to show the numbers. Use tens and ones to add. Stuart has 34 stickers. He gets 42 more. How many stickers does he have now?” Students are given a tens and ones diagram.

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. 

Each module contains two types of lessons specifically designed to engage students with conceptual understanding, Spark Your Learning and Bridging Lessons. The instructional materials present multiple opportunities for students to develop and conceptual understanding, and examples include:

• Module 2, Lesson 2, Count Back, begins with students working in pairs and using connecting cubes, counters, or drawing pictures to show subtraction. During Build Understanding, students use manipulatives and pictures to count back, solve, and write an equation to solve the problem. (1.OA.5)
• Module 2, Lesson 4, students use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums. In the Teacher’s Edition, "Select children who have used various strategies and tools to share with the class how they solved the problem. Have children discuss why they chose a specific strategy or tool." (1.OA.6)
• Module 6, Lesson 2, Spark Your Learning, students represent the number of animal cards in two different ways using counters, connecting cubes, or pictures. For example, “Liz has 9 animal cards. They are elephant cards and tiger cards. How many of each animal card could she have?” (1.OA.1)
• Module 9, Lesson 1, students choose a tool to represent teen numbers using tens and ones. Students use a ten frame to answer "How many counters fill a ten frame?" and "How does the quick picture help you know the value of a number?" (1.NBT.2)

The instructional materials present multiple opportunities for students to demonstrate conceptual understanding, examples include:

• Module 7, Lesson 3, students select and draw a number of counters that are more than 3 and fewer than 10. Students then show 3 fewer counters. Students use pictures, counters, and equations to deepen their understanding of unknown problems. (1.OA.1)
• Module 10, Lesson 1, students represent a two digit number using a picture or base ten blocks. They then write the number of tens and ones in the number. (1.NBT.2)
• Module 17, Lesson 2, students compare the length of objects to the length of a string and determine if the string is longer or shorter. Students answer, "How will you use the string and the objects you chose as tools to compare length?" Students also compare the lengths of objects and draw to show which objects are longer or shorter. (1.MD.1)

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

 Students develop procedural skills and fluencies throughout the grade level. Each module contains Procedural lessons that help students develop the steps in a procedure and determine when the procedure should be used. Module and Lesson components that specifically attend to student’s developing and independently demonstrating procedural skill and fluency include:

• In Module Planning: Teaching for Success, Teacher to Teacher notes give the teacher advice on how to question the student in order to build procedural fluency. For example, in Module 6, Teacher to Teacher, suggests having students think about the problem 12 - 5. The teacher asks questions about what equation they could write and how they would use tally marks to solve the problem. (1.OA.1)
• Module 3, Lesson 1, students use pictures and equations to represent addition in other ways using the commutative property of addition. Check Understanding, Problem 1, “Ron Plants 3 white rose bushes and 9 red rose bushes. How many rose bushes did he plant? ____=____+____ or ____=____+____rose bushes.” (1.OA.3)
• Module 8, Lesson 7, Step It Out , students use information from a chart to solve a problem using tally marks to show how many flowers are in different vases. “How do you know how many tallies to make for Vicki? What is one way to use the tally chart to tell whether Lian or Marcy put more flowers in the vase?” (1.MD.4)

 Unit 1 addresses 1.OA.6, add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Students build fluency through adding 10 and more, making a 10 to add, adding doubles, and using known sums to add. For example:

• Module 1, Lesson 4, On Your Own, Problems 4-9 , students “make ten” to add within 20. Students fluently build 10 and add the remaining value.
• Module 2, Lesson 2, Learn Together and Independent Practice, address addition and subtraction within 20, demonstrating fluency for addition and subtraction within 10 when students use a number line to count back to subtract and solve numerous subtraction problems.
• Module 3, Lesson 7, Step It Out, students find the sum of number cubes to develop fluency within 10 and apply that fluency to find sums within 20. In On My Own, Problem 4, students show three different ways to make 10. and students develop fluency of addition within 10.

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for teachers and students spending sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

Students engage in routine application problems throughout the grade level. In Independent Practice and On Your Own, students apply what they have learned to solve real world problems independently. For example:

• In Module 1, Lesson 7, Independent Practice, students draw and solve, “Julian has 7 marbles. His brother gives him 4 more. How many marbles does Julian have now?” (1.OA.1)
• In Module 2, Lesson 6, Check Understanding, students write an equation and explain the strategy they used to solve a word problem. “Nate has 14 apples. He gives 5 of them to friends. How many apples does he have now?” (1.OA.1)
• In Module 7, Lesson 6, students solve, “There are 13 blueberries. There are 8 more blueberries than cherries. How many cherries are there? Use a strategy to solve the problem. Draw or write to show the strategy. There are ___ cherries.” (1.OA.6) 
• In Module 8, Lesson 2, On Your Own, students use colored marbles to create a graph, interpret the data, and reason about the data. (1.MD.4)
• In Module 12, Lesson 8, students Use Mental Math to Make 10 Less and 10 More. During Independent Practice, students solve, “Susan, Tracy, and Kris each have a rock collection. Susan has 48 rocks in her collection. Tracy has 10 more rocks than Susan. Kris has 10 more rocks than Tracy. How many rocks do Tracy and Kris each have?” (1.NBT.5)

Examples of non-routine application of the mathematics include: 

• In Module 3, Lesson 5, On Your Own, Problem 8, students write their own word problem with three addends, and then solve it. (1.OA.2)
• In Module 5, Lesson 4, students “Write a story problem for the equation. Solve the problem. 17 - 8 = ?” (1.OA.1)
• In Module 6, Lesson 7, Independent Practice, students respond to “Cindy sees 13 butterflies. Some are orange and some are blue. How many butterflies could be orange, and how many could be blue?" Students are given a bar model to help them solve. (1.OA.1)

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for the three aspects of rigor not always being treated together and not always being treated separately. Overall, two or all three of the aspects are interwoven throughout each module.

All three aspects of rigor are present independently throughout the program materials. Examples include:

• In Module 1, Lesson 3, students develop procedural skill and fluency of addition within 20. (1.OA.6)
• In Module 5, Lesson 1, students develop conceptual understanding as they use objects and drawings to solve add to and take from problems where the results are unknown. (1.OA.1)
• In Module 5, Lesson 4, students solve add to and take from application problems. “Bert has some markers. He gives 8 to Alex. Now he has 5 markers. How many markers does he have to start?” (1.OA.1)

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. Examples include:

• In Module 4, Lesson 3, students develop conceptual understanding of related facts using two color connecting cubes, and they develop fluency in writing related addition and subtraction equations. (1.OA.6)
• In Module 7, Lesson 7, Step it Out, Problem 5, students use procedural skills and visual models to solve difference unknown word problems. “Sasha has 12 paper clips. Thomas has 7 fewer paper clips than Sasha. How many paper clips does Thomas have?” Students are prompted to use and draw counters and write an equation. (1.OA.1)
• In Module 9, Lesson 1, Build Understanding, Task 1, students build conceptual understanding using a variety of strategies to represent word problems. “There are 6 ladybugs on a bush. 6 more ladybugs join them. How many ladybugs are there now? Part A: How can you make a concrete model to solve the problem? Draw to show what you did. Part B: A quick picture uses sticks and circles to show tens and ones. How can you draw a quick picture to show the number of ladybugs?” (1.NBT.B.2)

The instructional materials reviewed for HMH Into Math Grade 1 partially meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout the grade-level.

All MPs are identified throughout the materials. There are some over identifications of MP1 and MP5 as they are identified as being present in every lesson. For example:

• MPs are identified in both the Planning and Pacing Guide and the Teacher Edition. 
• In the Teacher Edition, MPs are identified by using headings such as Persevere, Reason, Attend to Precision, Use Repeated Reasoning, Use Tools, Use Structure, and Model with Mathematics.
• The Planning and Pacing Guide explains each MP and provides a correlation to specific lessons. All Spark Your Learning lessons are labeled as Persevere (MP1). Planning and Pacing Guide, page PG64, says “Included in every lesson.” According to the Planning and Pacing Guide, Use Tools (MP5) is “In every Spark Your Learning and Module Review.”

In each lesson, Focus and Coherence identifies the MPs within the lesson, and the MPs are also identified throughout the lesson before a task. Because the identification is associated with a task, there are connections to grade level content. For example:

• Module 6, Lesson 4, Build Understanding, Task 1, identifies MP2, “Reason- Help children think about how numbers relate to the bar model. Children are being introduced to the bar model for the first time. Show children how to read the bar model.” 
• Module 8, Lesson 2, Step It Out, Task 2, identifies MP6, “Attend to Precision- Ask children what would happen if they did not complete their picture graph correctly. Discuss how being precise in counting and making their graph is important and that the graph will not be helpful if there are mistakes. Then read the problem aloud.” 
• Module 3, Lesson 3, Build Understanding, Task 1, identifies MP7, “Use Structure- Read and discuss the problem. Allow children to use connecting cubes. Discuss with children how they can use what they know about addition to help them solve this problem.”
• In Module 15, Lesson 3 identifies MP5 and MP6. In Build Understanding, Task 3-4, indicates MP6, "Describe how you can use 4 small squares to make a large square." and "You combined 4 squares to make a larger square. How could you combine those same 4 squares to make a rectangle that is not a square?"

Some lessons include an explanation about the connection to the MPs in Professional Learning. For example, in Module 4, Lesson 1, MP2, “In this lesson, children begin to understand and utilize the inherent relationship between addition and subtraction. In order to increase mathematical fluency, children must learn to recognize that these operations are dependent upon each other and that one can be used to assist in solving problems related to the other.” 

In the Planning and Pacing Guide, a summary of how the program features address each Mathematical Practice and Process standard are listed on Pages PG18 - PG19. There are also “Questions to Ask” to support each MP. For example:  

• MP 7: Look for and make use of structure identifies “Turn and Talk: prompts students to identify, describe, or explain a structure they used to solve a problem.” Questions to Ask identify ways to extend thinking of MP 7, “What rule did you use to make…? Why can you use that property in this problem? How is that like…?”

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for carefully attending to the full meaning of each practice standard (MP). 

The materials attend to the full intent of the MPs. Examples of the instructional materials attending to the full meaning of the MPs include:

• MP1: In Module 4, Lesson 2, Build Understanding,Task 1, “What are some ways you can use your concrete model to help you work through this problem? How do you know the facts you wrote in Part B are related facts? ”
• MP2: In Module 3, Lesson 5, On Your Own , Problem 7, “Reason: Find the unknown addend. Complete the equation. 1 + 3 + __ = 5.”
• MP4: In Module 6, Lesson 7, Step It Out, Task 2: “Lia has some animal books. She gives 9 books to Max. Now she has 5 books. How many books did Lia start with?” Students are guided to create a visual model for the problem, write a model they can use to solve the problem and use the models to organize their thinking.
• MP5: In Module 2, Lesson 2, Spark your Learning, “Viktoria makes 7 picture frames. She gives 2 to her friend. How many picture frames does she have now? How can counting help you solve the problem” Teachers are guided to ask, “Which tool could you use to solve the problem? Why is the tool you chose the one that works for you?” 
• MP6: In Module 12, Lesson 5, Step It Out, Task 2, prompts teachers to “Encourage children to explain how their drawings show the problem and explain why it is important to be accurate in their drawings.” “There are 20 paint jars in a store. The store gets 34 more paint jars. How many paint jars does the store have?”
• MP7: In Module 15, Lesson 1, Build Understanding, Turn and Talk, “How is a rectangle and a square the same? How are they different?”
• MP8: In Module 2, Lesson 2, Build Understanding, Task 2, “A kangaroo is on step 6 and takes 2 jumps down. What step is the kangaroo on now?  How can you use the picture to show how to count back? B. How can you write an equation to solve the problem?”

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

Students have opportunities to construct viable arguments through activities such as explaining their thinking or justifying steps, and the materials prompt them to analyze the arguments of others. Examples include:

• In Module 8, Lesson 3, Build Understanding, Problem 1C, “Did more friends wear blue or orange shirts? Circle your answer. How do you know?”
• In Module 8, Lesson 5, On Your Own, Problem 3, “Reason. There are 12 children in art class. 5 children paint. The rest make clay pots. Andy made this bar graph to show the data. He made a mistake. Explain the mistake Andy made.”
• In Module 13, Lesson 3, Build Understanding, Turn and Talk, “How can you use tens and ones to solve a subtraction problem? Explain the steps you used to subtract 90 – 40.”
• In Module 15, Lesson 2, On Your Own, Problem 4, students “Construct Arguments: Explain how to draw a triangle.”
• In Module 17, Lesson 3, On Your Own, Problem 7, students “Construct Arguments: How do you know that you colored half of each shape?”
• In Module 17, Lesson 1, On Your Own, students “Construct Arguments: Mercer thinks she circled the longest pencil. What is her mistake?”

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

The materials provide teachers with Sample Guided Discussions, Turn and Talks, and Leveled Questions to assist teachers in engaging students in discourse. There is also some teacher guidance on how to lead discussions beyond the provided questions. Examples include: 

• In Module 4, Lesson 3, Learn Together, Turn and Talk states, “Have children name two other related facts and explain their thinking.”
• In Module 11, Lesson 1, Spark Your Learning, “Select children who used various strategies and tools to share with the class how they solved the problem. Have children discuss why they chose a specific strategy or tool..” 
• In Lesson 16.2, More Practice/Homework Problems 1 and 2, the materials prompt teachers to ask students, “How do you know the shares are equal? and How do you know the shares are unequal?”

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for attending to the specialized language of mathematics. The materials provide explicit instruction on communicating mathematical thinking with words, diagrams, and symbols. The materials use precise, accurate terminology and definitions when describing mathematics and support students in using them. 

The Planning and Pacing Guide has a section for Language Development that states HMH Into Math is built upon 4 design principles to promote the use and development of language:

• Principal 1: Support Sense-Making;
• Principal 2: Optimize Output to help students describe their mathematical reasoning and understanding;
• Principal 3: Cultivate Conversations to facilitate mathematical conversations among students; and,
• Principal 4: Maximize Linguistic and Cognitive Meta-Awareness to help students evaluate their use of language and see how mathematical ideas, reasoning and language are connected.

Language Routines and new/review vocabulary are summarized on the Language Development page for each module, and this also includes Key Academic Vocabulary for Prior Learning - Review Vocabulary and Current Development - New Vocabulary with definitions. Also in Language Development, Linguistic Notes provide teachers help with possible misconceptions relating to academic language. For example:

• In Module 5, the Linguistic Note states, “As children solve various problem types using addition or subtraction, they may lack the language to express what is unknown. Work with children to identify Add To and Take From Result Unknown, Change Unknown, and Start Unknown problem types.” Module 6 includes Review Vocabulary: equation.
• Module 7 includes Key Academic Vocabulary, more and fewer.
• In Module 12, the Linguistic Note states, “The language in a math textbook can be challenging for English Language Learners. Many mathematics terms have multiple meanings. Taking time to distinguish between the meanings of these terms will help avoid confusion when asking questions, such as How many tens in 34? Taking time to distinguish between the meanings of these terms will help avoid confusion when asking questions about tens and ones.”
• In Module 17, the Linguistic Note states, “the math topics for measurement and data are rich with opportunities for cooperative grouping and language development. Take time prior to a lesson to highlight key vocabulary. For example, make sure children understand the suffixes -er and -est as used to compare objects by length.”

The Guided Student Discussion often provides prompts related to understanding vocabulary, for example, Lesson 4.3, Sample Guided Discussion, Persevere, “How do you know if facts are related to each other?”

Student pages include vocabulary boxes defining content vocabulary. Vocabulary is highlighted and italicized within each lesson in the materials. The vocabulary review at the end of each Module requires students to match new vocabulary terms with their meaning and/or examples provided, fill-in-the-blank with definitions or examples, or create a graphic organizer to help make sense of terms. Some lessons include Vocabulary Review. Connect Math Ideas, Reasoning, and Language Compare and Connect encourage students to use vocabulary terms to discuss mathematics with correct terminology. For example:

• In Module 2, Lesson 2, Count Back is highlighted in yellow and a visual model of counting back with counters and an equation is represented. 
• In Module 3, Lesson 6, students draw pictures to define equal and unequal. 
• In Module 8, Lesson 3, Connect Math Ideas, Reasoning, and Language Compare and Connect states, “Before beginning this task, have children define the terms tally chart, tally marks, and tallies in their own words. Encourage children to point to examples.”
• In Module 14, Lesson 1, Build Understanding, Connect Math Ideas, Reasoning, and Language Compare and Connect states, “Have children describe the shape of a cube and a rectangular prism. Have partners share their work and discuss how their descriptions compare and contrast.”

Vocabulary cards can be used with vocabulary games. The eGlossary includes vocabulary terms and definitions translated into ten different languages. The Interactive Glossary provides the definition and a visual (diagrams, symbols, etc.) is provided for each vocabulary word.The Interactive Glossary also provides space for students to make graphic organizers or drawings for each new vocabulary term. In the student materials, the instructions state, “As you learn about each new term, add notes, drawings, or sentences in the space next to the definition. Doing so will help you remember what each term means.”

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations that there is a clear distinction between problems and exercises in the materials.

The materials distinguish between problems and exercises within each lesson. Lessons include Spark Your Learning or Step it Out, Turn and Talk, Build Understanding, Check Understanding, and On Your Own, and More Practice/Homework. Spark Your Learning Problems activate prior knowledge and introduce new mathematics to students. Build Understanding includes problems that help students build conceptual understanding of the mathematics topic being taught. Check Understanding and On My Own sections include exercises that ask students to use the newly learned mathematics in each lesson. Additional practice and Homework is available in a separate Student Edition, providing more exercises for students to solve.

Each Module presents lessons with a consistent structure. During Build Conceptual Understanding, and Connect Concepts and Skills, students have opportunities to learn new content through problems and examples in guided instruction, step-by step procedures, and problem solving.

At the end of the lesson, On Your Own, More Practice/Homework, and Additional Practice provides a variety of exercises which allow students to independently show their understanding of the material. Exercises are designed for students to demonstrate understanding and skills in application and non-application settings. Test Prep and Spiral Review also include exercises.

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations that the design of assignments is intentional and not haphazard.

Overall, lessons are intentionally sequenced and scaffolded so students develop their understanding of mathematical concepts and skills. The structure of a lesson provides students with the opportunity to activate prior learning, build procedural skills, and engage with multiple activities that utilize concrete and abstract representations and increase in complexity.

Exercises are given in intentional sequences. In general, lessons are designed to begin with activating prior knowledge and build toward conceptual development and procedural skill. In Spark Your Learning, students use manipulatives and/or visual models to engage with the mathematical content, developing a concrete or representational understanding. This is followed by a Turn and Talk with a partner where students process the connections they have found. Throughout the lessons, students are provided scaffolding with new content in Build Understanding and Step It Out, where the abstract concept is broken down into smaller steps with additional Turn and Talks, and students complete independent exercises to build understanding and mastery. Check Understanding provides a mid-lesson check in and can be used to indicate the need to differentiate learning for students. Students solve and practice concepts in On Your Own, and More Practice/Homework.

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations for having a variety in what students are asked to produce.

In Spark Your Learning, Build Understanding, and Step It Out, students use visuals to show their thinking. In Turn and Talks, students frequently construct arguments, and explain why. There are opportunities for students to produce answers and solutions in On Your Own, while also providing opportunities for students to provide written explanations. Throughout the materials, students represent mathematics using equations.

The instructional materials reviewed for HMH Into Math Grade 1 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The Planning and Pacing Guide, Manipulatives and Tools, explains how manipulatives are used in each module.  The materials identify the manipulatives needed at the beginning of each lesson, and on student pages there is a picture of the manipulative they will use.  Examples of manipulatives for Grade 1 include: base ten blocks, connecting cubes, pattern blocks, square dot paper, and counters.

The visual design of HMH Into Math Grade 1 is not distracting or chaotic. The printed and digital materials follow a consistent format. Teacher editions provide information for teachers to be able to access digital resources. There is room for students to record answers and show their thinking.

Features of the materials are consistently presented, and the use of colored fonts supports identification of lesson components. Components of the lesson are labeled in the Teacher Edition as Part 1: Spark Your Learning, Part 2:  Learn Together, Part 3: Check Understanding, Part 4: Differentiation Options, and Part 5: Wrap Up.  For example, Turn and Talks are highlighted in yellow, and Check for Understandings are always in orange font. Visual images mirror the situation in the problem or can be used by students as they solve the problem.

Tasks within a lesson are numbered to match the module and lesson numbers. Student practice problem pages include enough space for students to write their answers and provide explanations.

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations for providing quality questions to help guide students’ mathematical development. 

Throughout the Teacher Edition, questions are posted to help support teachers with questions to guide students’ mathematical development. Activate Prior Knowledge, Spark Your Learning, Build Understanding, On Your Own, and Turn & Talk consistently provide questions to drive student discussion. 

• Module 7, Lesson 1, Learn Together provides the following questions for teachers: “How does the equation model show how you solved the problem? How could you use an addition equation to model the problem?”, and the leveled questions: “Who has fewer tennis balls in Task 2? How does using drawings or counters help you solve the problem? Why can an addition and a subtraction equation model the same problem?”
• Module 18, Lesson 4, Step it Out, provides the following questions for teachers: “For time to the hour, where is the hour hand pointing? Where is the minute hand pointing? How do you know where to point the hour hand? How do you know where to point the minute hand?”

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations for containing ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials.

In the Module planning pages, there is a variety of information that can help teachers understand the materials in order to present the content. Each lesson identifies the relevant content standards and Mathematical Practices, an I Can Statement, Learning Objective, Language Objective, materials needed, and Mathematical Progressions that contain prior learning, current development, and future connections. 

Unpacking the Standards provides further explanations of the standards’ connections. This section gives an explanation of the content standard contained in the lesson and Professional Learning, which sometimes contains information about the practice standard contained in that lesson. Teaching for Depth provides teachers with information regarding the content and how this relates to student learning.There are additional suggestions about activating prior knowledge or identifying skills in Warm-up Options, activities to Sharpen Skills, Small-Group Options, and Math Centers for differentiation.

The instructional materials reviewed for HMH Into Math Grade 1 partially meet the expectations for containing adult-level explanations so that teachers can improve their own knowledge of the subject. 

The materials include adult-level explanations of the grade-level content, but the materials do not include adult-level explanations of advanced mathematics concepts so that teachers can improve their own knowledge of the subject.

The materials include explanations and examples of the course-level mathematics specifically for teachers that can improve their own knowledge of the subject. In the Teacher Edition modules, there are examples and support for the adult in the math classroom as it relates to grade-level standards. For example: 

• The Mathematical Progressions table in each module and lesson, highlights Prior Learning, Current Development and Future Connections.
• Planning and Pacing includes a correlation chart for the math practices that defines each math practice in full.
• Every Module introductory pages include Teacher for Depth and Teacher to Teacher. Every lesson includes either Professional Learning (About the Math, Using Mathematical Practices and Processes, and Visualizing the Math) and/or Unpacking Math Standards. 
• Professional Learning videos are available online on Ed: Your Friend in Learning. This is noted on each Module Planning Page A of the Teacher Edition.

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations for explaining the role of grade-level mathematics in the context of the overall mathematics curriculum.

Each module in the Teacher Edition includes Mathematical Progressions which lists prior learning, current development, and future connections. Similarly, the beginning of each lesson in the Teacher Edition includes Mathematical Progressions that show connections to prior and future grades’ standards, as well as other lessons within the program.

In the Planning and Pacing Guide, Progressions and Algebra Readiness notes “Algebra as a course of study today is integrated around four progressions of elementary and middle school content leading to the Algebra course: Number and Operations, Operations and Algebraic Thinking, Statistics and Probability, and Functions” and includes a table that shows how the domains in Grades K-5, 6-7, and Grade 8 / Algebra fit into these progressions.

The instructional materials reviewed for HMH Into Math Grade 1 provide a list of lessons in the teacher's edition, cross-­referencing the standards addressed, and a pacing guide. 

The Planning and Pacing Guide includes the standards and pacing (number of days) for each lesson. There is another standards chart in the Planning and Pacing Guide that lists each standard and correlation to Student Edition Lessons. In the Teacher Edition, pacing is provided in the module planning pages, with written descriptions of the standards, as well as listed under Current Development in the Mathematical Progressions chart.

The instructional materials reviewed for HMH Into Math Grade 1 include strategies for parents to support their students progress. The Family Resources tab includes several resources for parents:

• “School Home Letters  inform families about the skills, strategies, and topics students are encountering at school.” Each module includes a letter, found online in 4 languages, providing vocabulary, a home activity, and discussion prompts. This letter is available in English, Spanish, Haitian-Creole, and Portuguese.
• Math on the Spot videos are available for specific lessons within a module.

The instructional materials reviewed for HMH Into Math Grade 1 explain instructional approaches used and how they are research based.

The Planning and Pacing Guide contains Teacher Support Pages that include a section on Supporting Best Practices. “Into Math Florida was designed around research-based, effective teaching practices such as those described in Principles to Actions (NCTM 2014).” These include:

• Establish mathematics goals to focus learning.
• Implement tasks that promote reasoning and problem solving.
• Use and connect mathematical representations.
• Facilitate meaningful mathematical discourse.
• Pose purposeful questions.
• Build procedural fluency from conceptual understanding.
• Support productive struggle in learning mathematics.
• Elicit and use evidence of student thinking.

The Planning and Pacing Guide describes four design principles from the Stanford Center for Assessment, Learning, and Equity (SCALE) that “Into Math classrooms maximize student growth by helping teachers deliver high quality instruction while monitoring every student’s success.” These principles are: Support sense-making; Optimize output; Cultivate conversation; and Maximize linguistic and cognitive meta-awareness. To address this, the instructional materials include language routines that “help teachers promote the design principles during instruction.” Each module contains a Language Development page in the Teacher Edition that states where the language routines should be used. On the lesson pages of the Teacher Edition, there are Support-Sense Making boxes that describe how the language routine can be used. Also, there are notes in the margin of the teacher’s edition providing connections from the strategy to the principle.

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels.

• At the beginning of the year, students’ prior knowledge is gathered through a Prerequisite Skills Inventory. “This short-answer test assesses core precursor skills that are most associated with on-grade success.” (Assessment Guide)
• Each module begins with Are You Ready, a diagnostic assessment of prior learning related to the current grade-level standards. Intervention materials are provided to assist students not able to demonstrate the necessary skills. Commentary for each standard explains how the prior learning is relevant to the current module’s content. 
• Prior learning is identified in the Mathematical Progressions section at the beginning of each module and lesson in the Teacher Edition.

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

• The module overview in the Teacher Edition contains Common Errors as students engage in an introductory task and provides questioning strategies intended to build student understanding.
• The Spark Your Learning planning page for each lesson in the Teacher Edition includes Common Errors related to the content of the lesson that identifies where students may make a mistake or exhibit misunderstanding. There is a rationale that explains the likely misunderstanding and suggests instructional adjustments or steps to help address the misconceptions. 
• There are also Watch Fors and question prompts that highlight areas of potential student misconceptions.

The instructional materials reviewed for HMH Into Math Grade 1 partially meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The materials provide support for ongoing review and practice.

• Within each lesson there are activities to Activate Prior Knowledge. The Math Routine is a review problem from prior units/lessons. Make Connections provides teacher support on next steps based on the students’ responses.
• Sharpen Skills provides ongoing fluency practice.
• Test Prep questions “provided are intended to assess the child’s ability to extend understanding…”
• In Homework/Practice, Spiral Review is designed to “help determine if children have retained information taught in the past.” 
• Online interactive lessons and homework practice provide students with immediate notification if their answers are correct/incorrect.

There is no specific feedback to students or guidance for teachers on how to interpret and give feedback to students for the Sharpen Skills, Test Prep, and Spiral Review.

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations that assessments clearly denote which standards are being emphasized. 

The Lesson Focus and Coherence page indicates the CCSSM that will be addressed within the Lesson. Throughout the lesson, there are formative assessments in Check for Understanding, On Your Own, and More Practice/Homework. Each lesson has a diagnostic assessment, Are You Ready, correlated to standards.

Each Module has an End of Module Test, and the standards associated with each problem on this test can be found on the Individual Record Form within the Assessment Guide Book. In addition, Assessment Preparation includes Standards-Based Practice for most lessons.

Each Unit has a summative Performance Task that includes the content focus in the teacher pages of the Assessment Guide.

The instructional materials for reviewed HMH Into Math Grade 1 meet the expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Each lesson has a diagnostic assessment, Are You Ready, and the materials state that teachers can use Online Ed, to assign the Digital Are You Ready? to power actionable reports including proficiency by standards item analysis.

The Planning and Pacing Guide notes, “Check Understanding is a quick formative assessment in every lesson. Teachers use data to determine which students need additional small-group support and which students can continue on to independent practice or math center challenges.” 

Each performance task includes a task-specific rubric indicating a level 0 response through a level 3 response. The structure of the rubrics is the same, but specific words are changed to reflect the mathematical content of the module. Level 3 indicates that the student made sense of the task, has complete and correct answers, and checked their work or provided full explanations. Level 2 indicates that the student made sense of the problem, made minor errors in computation or didn’t fully explain answers. Level 1 indicates that the students made sense of some components of the task but had significant errors in their solution strategies. Level 0 shows little evidence that the student has made sense of the task, addressed specific components,and does not complete the problem. The Planning and Pacing Guide indicates a content focus for each of the items on the Unit Performance Tasks.  Each content area is identified with a depth of knowledge as well as one or more Reteach pages for follow-up with students. 

The Individual Record Forms in the Assessment Guide suggest Reteach Lessons that teachers can use for follow-up based on the Module assessments and Performance Assessments.

The Individual Record Forms for the Prerequisite Skills Inventory, Beginning-of-Year, Middle-of-Year Test, and End-of-Year Tests do not suggest Reteach Lessons or provide other guidance that teachers can use for follow-up with students.

The instructional materials reviewed for HMH Into Math Grade 1 include Scales to Track Learning Goals at the end of each lesson. The Teacher Edition introduction states, “The scales below can help you and your students understand their progress on a learning goal. Scales are also available in Module Resources.” 

Each lesson contains “I can” scales with four levels of “I Can” statements written in increased difficulty. While there is a note saying, “The scale below can help you and your students understand their progress on a learning goal.” There is no explicit indication of how to use these scales. 

At the end of On Your Own, there is Learning Mindset where students write a response to reflect on the lesson.

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. 

Throughout the materials, strategies are present, with guidance in the beginning of each module and lesson for both teachers and students. Examples include: 

• Teaching for Depth provides information on strategies to use when teaching the concept. Represent and Explain focuses on ways for students to describe and picture a concept. Make Connections helps students understand a new idea by connecting it to previous knowledge.
• Mathematical Progressions make connections to both prior and future skills and standards to scaffold instruction.
• Diagnostic Assessment, Are You Ready?, allows teachers to “diagnose prerequisite mastery, identify intervention needs, and modify or set up leveled groups.”
• Each lesson provides Warm-up Options to activate prior knowledge such as Math Routines and Make Connections.
• Throughout the lessons, there are notes, strategies, sample guided-discussion questions, and possible misconceptions that provide teachers structure in making content accessible to all learners.
• In each lesson, Check for Understanding problems provide information on student understanding of the lesson content, before they begin independent work during On Your Own.

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

• There are Reteach and Challenge activities for each lesson.
• Each lesson includes Plan for Differentiated Instruction that provides teachers with teacher-guided, Small-Group Options and self-directed Math Center Options based on student need: “On Track, Almost There (RtI), and Ready for More.”
• Each lesson provides Leveled Questions identified as DOK 1, 2, and 3 with an explanation of the knowledge those questions uncover about student understanding.
• In the Teacher Edition, Spark Your Learning provides two possible strategies and a common error. Each section describes student actions and has teachers either describe and practice or remind them of important strategies to support learning and how to intervene..

There are four “Language Routines to Develop Understanding” used throughout the materials: 

• “Three Reads: Students read a problem three times with a specific focus each time.” 
• “Stronger and Clearer Each Time: Students write their reasoning to a problem, share, explain their reasoning, listen to and respond to feedback, and then write again to refine their reasoning.”  
• “Compare and Connect: Students listen to a partner’s solution strategy and then identify, compare, and contrast this mathematical strategy.” 
• “Critique, Correct and Clarify: Students correct work that is not their own with a flawed explanation, argument, or solution method and share with a partner to reflect and then refine the sample work.”

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

STEM Tasks are provided at the beginning of every instructional unit and include cross-curricular tasks which allow multiple entry-points and various solution strategies or representations, for example:

• In Unit 5, STEM Task: “Have children study the picture on page 414 and identify the two-dimensional shapes that they see on the table. Challenge them to use all of the shapes shown in the picture to draw and color a logo. Show children various examples of logos to get them started. Ask children to discuss how the different logos they see communicate different ideas. Have children think about the idea or mood that they would like their logo to communicate. Give children the opportunity to receive feedback and revise their logo once they are finished.”

Turn and Talks throughout each lesson provide opportunities for students to share a variety of ways to solve the problem, for example:

• In Module 16, Lesson 3, Turn and Talk: “How do you know that the part you colored is one of the halves?”

In the Planning and Pacing Guide, Spark Your Learning tasks are “designed as ‘low-floor/high ceiling’ tasks that all students can access but that can also be extended to provide challenge.” Teachers are provided guidance on how to assist various levels of learners depending on how they respond to the problem.

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations for suggesting support and accommodations for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

In each module, Language Development provides support for ELLs including linguistic notes that provide strategies intended to help students struggling with key academic vocabulary such as: “Speak with students about words that can have multiple meanings….”, and “Visual cues help students…” Language Development also includes information about the Language Routines embedded in the instructional materials: Three Reads; Stronger and Clearer Each Time; Compare and Contrast; Critique, Correct, and Clarify. These are identified by a pink box throughout lessons with a speech bubble that identifies the Language Routine to be used. In addition, there are supports for special populations including:

• Language Objectives are included in every lesson.
• Reteach and RtI worksheets can be assigned online or printed.
• Turn and Talk prompts designed to support students, for example, “Go back and reread the problem and break it into pieces. For example: What do you know? What do you need to find?”
• A multilingual glossary is available online.

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

Supports for advanced students include:

• Each lesson has a corresponding Challenge page, provided in print or online, addressing the same concepts and standards where students further extend their understanding. 
• In the beginning of each module, Extend the Task provides suggestions for deeper exploration of the tasks.

The instructional materials reviewed for HMH Into Math Grade 1 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

Pictures of adults and children in the materials show a variety of demographics and personal characteristics. There are a variety of names used in word problems throughout the materials. The lessons contain a variety of tasks and situations in the story problems that interest students of various demographic and personal characteristics. There is a balanced approach to the use of gender identification. Examples include:

• The materials reference roles instead of pronouns (e.g., the players, book fair, sailboats, collection of toy cars, piggy banks, carton of eggs).
• The materials include a set number of names used throughout the problems and examples (e.g., Janette, Anton, Zed, Ari, Tai, Nick, Sam). These names are presented in a way that does not stereotype characters by gender, race, or ethnicity.

The instructional materials reviewed for HMH Into Math Grade 1 provide opportunities for teachers to use a variety of grouping strategies.

In the Planning and Pacing Guide there is a section titled, “Grouping and Recommendations. This section states, “One of the most valuable and time-saving tools for teachers is the online Recommend Groups feature. It synthesizes data from assessments and places students into leveled groups. You can easily modify the recommended groups yourself as needed.” 

• Each lesson provides teachers with a differentiated plan that includes small-group options. 
• The materials provide students with self-directed activities at math centers.
• Throughout the materials, there are ample opportunities for students to Turn and Talk with a partner. 
• Using the Check for Understanding, the teacher is directed to pull students into small groups and use the Teacher Tabletop Flipchart.

The instructional materials reviewed for HMH Into Math Grade 1 encourage teachers to draw upon home language and culture to facilitate learning.

The student Interactive Glossary is available in both English and Spanish, and  School-Home Letters are available in English, Spanish, Haitian-Creole, and Portuguese. Examples of home language connections and connections to assist in embracing the culture of students are present to assist in facilitating student learning.

The instructional materials reviewed for HMH Into Math Grade 1 include interactive lessons that can be found in online practice on the digital platform. The interactive lessons include drag and drop options, multiple-choice questions, and click-on-the-correct item questions. Students are able to submit their completed assignment for teacher feedback via the digital platform.

Interactive Lessons are provided online for each lesson. Audio is provided to read each page. Students can draw pictures. (Note: Students using a computer must use the mouse to draw.) For example, in Lesson 1.5, Build Understanding, Interactive Lessons, students draw or add shapes to solve the word problem. The problem can be read aloud to them. Some interactive taks provide in-time feedback to students as they answer questions telling them “That strategy you used worked! Great effort!”, if given a correct answer

No virtual manipulatives were found in the online lessons. Some lessons do include the draw or add a shape interactive tools.

The instructional materials reviewed for HMH Into Math Grade 1 are web-based and compatible with multiple Internet browsers.

• The materials are platform-neutral and compatible with Chrome, ChromeOS, Safari, and Mozilla Firefox.
• Materials are compatible with iPads, laptops, Chromebooks, and other devices that connect to the internet with an applicable browser. Online use was difficult on a Chromebook with scrolling and loading issues as well as difficulty seeing all pieces of the interactive editions.
• The materials are not compatible with an Android device (using Chrome browser). Although the website can be reached, it is not possible to zoom in or out, nor can one move the screen, so a student cannot access the entire screen.

The instructional materials reviewed for HMH Into Math Grade 1 include opportunities to assess student mathematical understanding and knowledge of procedural skills using technology through a website called Online ED, which parallels the print textbook. Only one module per grade is currently available in the digital format, so some of the evidence is stated in the materials but has not actually been observed.

• Lesson problems from the Student Edition, assessments, and unit performance tasks are provided to be completed and scored using technology, providing students with feedback on whether the answers are correct or incorrect.
• Online Ed is designed to make recommendations for differentiation after auto-scoring of Check Understanding problems within each lesson. 
• Growth monitoring assessments are “designed to be administered in 40 minutes, 3 times per year. The system utilizes a secure bank of assessments to adapt to each student’s ability and maps progress on the Quantile Framework.” (Pacing Guide)
• Dynamic Reporting allows teachers to drill down into data for deeper insights into student performance. Assignment reports show detailed results for each assignment. Standard reports show progress towards mastery of each standard. Interim growth measure reports help identify intervention needs and link to recommendations and groupings. 
• Assessments can be created using a question bank that repeats the questions presented throughout the interactive lessons. However, teachers cannot modify questions nor add new questions.
• The online system has dynamic reporting by assignment or standards. If teachers are using the online system, they can view student progress for interim growth, module readiness, and lesson practice and homework.

The instructional materials reviewed for HMH Into Math Grade 1 are intended to include opportunities for teachers to personalize learning for all students. Full functionality of online materials is not accessible at the time of this review.

• Teachers can assign lesson problems and assessments, as well as view assessment analytics. 
• Teachers can group students according to individual needs. The online component has Recommended Groups that “synthesizes data from assessments and places students into leveled groups.” (Pacing Guide) Recommended lesson resources can be assigned to each group.
• Teachers can create assessments using a bank of items.

The instructional materials reviewed for HMH Into Math Grade 1 provide minimal opportunities to be adapted for local use. Full functionality of online materials is not accessible at the time of this review.

• Pieces of a lesson can be assigned directly to students or groups of students. 
• There is a question bank for teachers to create assessments. The bank repeats the questions that are already included in each lesson, and these questions cannot be modified.

The instructional materials reviewed for HMH Into Math Grade 1 do not incorporate technology that provides opportunities for multiple students to collaborate with the teacher or one another.